Statistical and numerical analysis of secondary electron avalanches with ion-induced electron emission in air

  • Suzana N. StamenkovićEmail author
  • Vidosav Lj. Marković
  • Marjan N. Stankov
  • Aleksandar P. Jovanović
Regular Article


Statistical and numerical analyses of secondary electron avalanches with ion-induced electron emission and multielectron initiation in air is carried out. Statistical analysis is based on the negative binomial distribution (NBD) and its mixtures and the mean number of electrons in avalanches is determined. The development of successive secondary electron avalanches for ion-induced electron emission from the cathode (\( \gamma_{i} \) process) in air is simulated by the fluid model. The statistics of secondary avalanches is described by a mixture of NBDs, and it is found that the mixing weights \( a_{j} \) are positively correlated with \( \mu^{j} \) for the contribution of secondary avalanche of \( j \)th generation, where \( \mu = \gamma_{i} [\exp (\alpha d) - 1] \) is the avalanche regeneration factor. Gaussian continual approximations for the discrete negative binomial distribution are also applied to the experimental data and the mixing weights are determined. Our models can explain a deviation of the electron number distribution from exponential due to influence of ion feedback processes.



The authors are grateful to the Ministry of Education, Science, and Technological Development of the Republic of Serbia for partial financial support (Projects OI 171025).


  1. 1.
    H. Raether, Electron avalanches and breakdown in gases (Butterworths, London, 1964)Google Scholar
  2. 2.
    E.E. Kunhardt, L.H. Luessen (eds.), Electrical breakdown and discharges in gases, part a, fundamental processes and breakdown; part b, macroscopic processes and discharges (Plenum Press, New York, 1983)Google Scholar
  3. 3.
    C. Grupen, I. Buvat (eds.), Handbook of particle detection and imaging (Springer, Berlin, 2012)Google Scholar
  4. 4.
    P. Fonte, V. Peskov, Plasma Sour. Sci. Technol. 19, 034021 (2010)ADSCrossRefGoogle Scholar
  5. 5.
    P. Crespo, A. Blanco, M. Couceiro, N.C. Ferreira, L. Lopes, P. Martins, R.F. Marques, P. Fonte, Eur. Phys. J. Plus 128, 73 (2013)CrossRefGoogle Scholar
  6. 6.
    F. Sauli, Gaseous radiation detectors, fundamentals and applications (University Press, Cambridge, 2014)zbMATHCrossRefGoogle Scholar
  7. 7.
    H. Furry, Phys. Rev. 52, 569 (1937)ADSCrossRefGoogle Scholar
  8. 8.
    R.A. Wijsman, Phys. Rev. 75, 833 (1949)ADSCrossRefGoogle Scholar
  9. 9.
    H. Schlumbohm, III Z. Phys. 151, 563 (1958)ADSCrossRefGoogle Scholar
  10. 10.
    J. Byrne III, Proc. Roy. Soc. Edinburgh Sect. A 66, 33 (1962)Google Scholar
  11. 11.
    L. Lansiart, J.P. Morucci, J. Phys. Phys. Appl. 23(Suppl. 6), 102 (1962)CrossRefGoogle Scholar
  12. 12.
    A.H. Cookson, T.J. Lewis, Brit. J. Appl. Phys. 17, 1473 (1966)ADSCrossRefGoogle Scholar
  13. 13.
    H. Genz, Nucl. Instr. Method. 112, 83 (1973). (and references therein) ADSCrossRefGoogle Scholar
  14. 14.
    G. Vidal, J. Lacaze, J. Maurel, J. Phys. D Appl. Phys. 7, 1684 (1974)ADSCrossRefGoogle Scholar
  15. 15.
    H. Legler, Z. Naturforsch. 19A, 481 (1964)ADSCrossRefGoogle Scholar
  16. 16.
    A.H. Cookson, B.W. Ward, T.J. Lewis, Brit. J. Appl. Phys. 17, 891 (1966)ADSCrossRefGoogle Scholar
  17. 17.
    G.D. Alkazov, Nucl. Instrum. Method 89, 155 (1970)ADSCrossRefGoogle Scholar
  18. 18.
    Y. Kondo, S. Kajita, S. Ushiroda, J. Phys. D Appl. Phys. 17, 1361 (1984)ADSCrossRefGoogle Scholar
  19. 19.
    Y. Kondo, J. Appl. Phys. 57, 995 (1985)ADSCrossRefGoogle Scholar
  20. 20.
    A.P. Jovanović, S.N. Stamenković, M.N. Stankov, V. Lj, Marković. Contrib. Plasma Phys. 59, 272 (2019)ADSCrossRefGoogle Scholar
  21. 21.
    S. N. Stamenković, V. Lj. Marković, A.P. Jovanović, M.N. Stankov, JINST 13, P12002 (2018)Google Scholar
  22. 22.
    V. Lj. Marković, S. N. Stamenković, A. P. Jovanović, JINST 14, P06009 (2019)Google Scholar
  23. 23.
    M.R. Spiegel, Shaum’s outline of theory and problems of probability and statistics (McGraw-Hill, New York, 1998)Google Scholar
  24. 24.
    N. Johnson, A. Kemp, S. Kotz, Univariate discrete distributions, 3rd edn. (Wiley, New Jersey, 2005)zbMATHCrossRefGoogle Scholar
  25. 25.
    D.D. Wackerly, W.I.I.I. Mendenhall, R.L. Schaeffer, Mathematical statistics with applications, 7th edn. (Duxbury Press, Belmont, 1996)Google Scholar
  26. 26.
    S.C. Bagui, K.L. Mehra, Am. J. Math. Stat. 6, 115 (2016)Google Scholar
  27. 27.
    G. Casella, R.L. Berger, Statistical inference (Duxbury, Pacific Grove, 2002)zbMATHGoogle Scholar
  28. 28.
    L.J. Bain, M. Engelhardt, Introduction to probability and mathematical statistics, 2nd edn. (Duxbury Press, Belmont, 1992)Google Scholar
  29. 29.
    G. Holst, E. Oosterhuis, Phil. Mag. 46, 1117 (1923)CrossRefGoogle Scholar
  30. 30.
    R. Seeliger, Naturwiss 16, 665 (1928)ADSCrossRefGoogle Scholar
  31. 31.
    R. Holm, Zeits. f. Physik 75, 171 (1932)ADSCrossRefGoogle Scholar
  32. 32.
    F. Ghaleb, A. Belasri, Radiat. Eff. Defects Solids 167, 377 (2012)ADSCrossRefGoogle Scholar
  33. 33.
    A. P. Jovanović, M. N. Stankov, V. Lj. Marković, S. N. Stamenković, Europhys. Lett. 104, 65001 (2013)Google Scholar
  34. 34.
    M. N. Stankov, M. D. Petković, V. Lj. Marković, S. N. Stamenković, A. P. Jovanović, Chin. Phys. Lett. 32, 025101 (2015)Google Scholar
  35. 35.
    R. Morrow, J.J. Lowke, J. Phys. D Appl. Phys. 30, 614 (1997)ADSCrossRefGoogle Scholar
  36. 36.
    G.E. Georghiou, A.P. Papadakis, R. Morrow, A.C. Metaxas, J. Phys. D Appl. Phys. 38, R303 (2005)ADSCrossRefGoogle Scholar
  37. 37.
    C. Ferrara, M. Preda, C. Cavallotti, J. Appl. Phys. 112, 113301 (2012)ADSCrossRefGoogle Scholar
  38. 38.
    J.P. Boeuf, Phys. Rev. A 36, 2782 (1987)ADSCrossRefGoogle Scholar
  39. 39.
    J.D.P. Passchier, W.J. Goedheer, J. Appl. Phys. 74, 3744 (1993)ADSCrossRefGoogle Scholar
  40. 40.
    G. Chen, L.L. Raja, J. Appl. Phys. 96, 6073 (2004)ADSCrossRefGoogle Scholar
  41. 41.
    F.H. Scharf, R.P. Brinkmann, J. Phys. D Appl. Phys. 39, 2738 (2006)ADSCrossRefGoogle Scholar
  42. 42.
    F.H. Scharf, R.P. Brinkmann, J. Phys. D Appl. Phys. 41, 185206 (2008)ADSCrossRefGoogle Scholar
  43. 43.
    F.H. Scharf, Fluid dynamic and kinetic modelling of the near-cathode region in thermal plasmas (Logos Verlag Berlin, 2009)Google Scholar
  44. 44.
    H. P. Langtangen and G. K. Pedersen, Scaling of Differential equations (Springer Open, 2016)Google Scholar
  45. 45.
    G. J. M. Hagelaar, L. C. Pitchford, Plasma Sources Sci. Technol. 14, 722 (2005), BOLSIG + CPAT: Accessed Apr 2017ADSCrossRefGoogle Scholar
  46. 46.
    D. Nelson, M. Benhenni, O. Eichwald, M. Yousfi, J. Appl. Phys. 94, 96 (2003)ADSCrossRefGoogle Scholar
  47. 47.
    A. Bekstein, M. Yousfi, M. Benhenni, O. Ducasse, O. Eichwald, J. Appl. Phys. 107, 103308 (2010)ADSCrossRefGoogle Scholar
  48. 48.
    R. Rao, G. Raju, J. Phys. D Appl. Phys. 4, 494 (1971)ADSCrossRefGoogle Scholar
  49. 49.
    K. Masch, Arch. Elektrotech. 26, 587 (1932)CrossRefGoogle Scholar
  50. 50.
    J.L. Moruzzi, D.A. Price, J. Phys. D Appl. Phys. 7, 1434 (1974)ADSCrossRefGoogle Scholar
  51. 51.
    S. Pancheshnyi, J. Phys. D Appl. Phys. 46, 155201 (2013)ADSCrossRefGoogle Scholar
  52. 52.
    Y. Tanaka, J. Phys. D Appl. Phys. 37, 851 (2004)ADSCrossRefGoogle Scholar
  53. 53.
    W. Wang, A. Bogaerts, Plasma Sour. Sci. Technol. 25, 055025 (2016)ADSCrossRefGoogle Scholar
  54. 54.
    W. Wang, A.B. Murphy, M. Rong, H.M. Looe, J.W. Spencer, J. Appl. Phys. 114, 103301 (2013)ADSCrossRefGoogle Scholar
  55. 55.
    Y. Wu, W.Z. Wang, M.Z. Rong, L.L. Zhong, J.W. Spencer, J.D. Yan, I.E.E.E. Trans, Dielectr. Electr. Insul. 21, 129 (2014)ADSCrossRefGoogle Scholar
  56. 56.
    M. Yousfi, N. Merbahi, F. Reichert, A. Petchanka, J. Appl. Phys. 121, 103302 (2017)ADSCrossRefGoogle Scholar
  57. 57.
    M. Yousfi, P. Jouan, Z. Kanzari, I.E.E.E. Trans, Dielectr. Electr. Insul. 12, 1192 (2005)CrossRefGoogle Scholar
  58. 58.
    J.D. Yan, M.T.C. Fang, Q.S. Liu, I.E.E.E. Trans, Dielectr. Electr. Insul. 4, 114 (1997)CrossRefGoogle Scholar
  59. 59.
    Z. Lj. Petrović, A. V. Phelps, Phys. Rev. E 56, 5920 (1997)ADSCrossRefGoogle Scholar
  60. 60.
    A.V. Phelps, Z. Lj, Petrović. Plasma Sour. Sci. Technol. 8, R21 (1999)CrossRefGoogle Scholar
  61. 61.
    Z. Donko, Phys. Rev. E 64, 026401 (2001)ADSCrossRefGoogle Scholar
  62. 62.
    A. Bogaerts, R. Gijbels, Plasma Sour. Sci. Technol. 11, 27 (2002)ADSCrossRefGoogle Scholar
  63. 63.
    D. Marić, M. Savić, J. Sivoš, N. Škoro, M. Radmilović-Radjenović, G. Malović, Z.Lj. Petrović, Eur. Phys. J. D 68, 155 (2014)ADSCrossRefGoogle Scholar
  64. 64.
    A. P. Jovanović, V. Lj. Marković, S. N. Stamenković, M. N. Stankov, J. Phys. D: Appl. Phys. 48, 465204 (2015)ADSCrossRefGoogle Scholar
  65. 65.
    A. Lyashenko, A. Breskin, R. Chechik, J.M.F. dos Santos, F.D. Amaro, J.F.C.A. Veloso, Nucl. Instrum. Methods A 598, 116 (2009)ADSCrossRefGoogle Scholar
  66. 66.
    B.K. Sing, E. Shefer, A. Breskin, A. Chechik, N. Avraham, Nucl. Instrum. Methods A 454, 364 (2000)ADSCrossRefGoogle Scholar
  67. 67.
    P. Breuil, P. Fonte, E. Nappi, R. Oliveira, V. Peskov, Eur. Phys. J. Plus 128, 160 (2013)CrossRefGoogle Scholar

Copyright information

© Società Italiana di Fisica (SIF) and Springer-Verlag GmbH Germany, part of Springer Nature 2020

Authors and Affiliations

  1. 1.Department of Physics, Faculty of Sciences and MathematicsUniversity of NišNišSerbia
  2. 2.Leibniz Institute for Plasma Science and Technology (INP)GreifswaldGermany

Personalised recommendations